Velocity scaling of a shock wave reflected off a circular cylinder

Two different approaches are undertaken to investigate the interaction of planar shock waves with circular cylinders. Experiments are conducted in a shock-tube apparatus equipped with a schlieren-based optical system to monitor the interaction, and numerical simulations are carried out using an in-house computer code to simulate similar problems. The incident shock-wave Mach number is varied in the range 1.1-1.4. Excellent agreement is found between the simulations and the experiments in terms of shock patterns, even though the model is based on an inviscid approach. Quantitative comparisons between the experimental results for different initial conditions (shock-wave strength, cylinder diameter, and working gas) are made to find the physical parameters affecting the path of the reflected shock. An approximate universal relation is derived, which predicts the reflected-shock trajectory along the axis of symmetry as a function of the incident-shock Mach, the diameter of the cylinder, and the gas properties. This relation is valid in the vicinity of the cylinder in the range of 0.1-5 D, where D is the cylinder diameter. It is found that the reflected shock from the cylinder evolves as in the case of a reflected-shock wave from a planar wall multiplied by a reduction factor, which depends on the incident-shock Mach number and the ratio of specific heats.